The probability of one hit on the target with one volley of two guns is 0.38. Find the probability

The probability of one hit on the target with one volley of two guns is 0.38. Find the probability of hitting a target with one shot by the first of the guns, if it is known that for the second gun this probability is 0.8.

Let the probability of hitting the first weapon be p1, and the probability of a miss – q1.
The probability of hitting the target for the second gun is p2 = 0.8;
Missing chance for second gun:
q2 = 1 – p2 = 1 – 0.8 = 0.2;
The probability that there will be one shot is equal to the sum of the probabilities that the first gun hit and the second missed, or that the second hit and the first missed.
P = p1 q2 + p2 q1;
0.38 = p1 0.2 + 0.8 (1 – p1);
0.38 = 0.8 – 0.6 p1;
0.6 p1 = 0.42;
p1 = 0.7;
Answer: The probability of hitting the target with one shot from the first gun is p1 = 0.7.



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